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Mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information.

Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.

definition

Aristotle defined mathematics as "quantitative mathematics", which lasted until18th century. /kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions.

Some of these definitions emphasize the deductive nature of a lot of mathematics, some emphasize its abstraction, and some emphasize some themes in mathematics. Even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided.

Many professional mathematicians are not interested in the definition of mathematics or think it is undefined. Some just said, "Mathematics is done by mathematicians." The three main mathematical definitions are called logicians, intuitionists and formalists, each of which reflects a different school of philosophical thought. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible.

The three main mathematical definitions are called logicians, intuitionists and formalists, each of which reflects a different school of philosophical thought. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible. The early definition of mathematical logic is BenjaminPeirce's Science of Drawing Inevitable Conclusions (1870).

In PrincipiaMathematica, BertrandRussell and AlfredNorthWhitehead put forward a philosophical program called logicism, trying to prove that all mathematical concepts, statements and principles can be defined and proved by symbolic logic. The logical definition of mathematics is Russell's "All mathematics is symbolic logic" (1903).